Problem: Simplify; express your answer in exponential form. Assume $q\neq 0, a\neq 0$. $\dfrac{{(q)^{-2}}}{{q^{-5}a^{2}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${q}$ to the exponent ${-2}$ . Now ${1 \times -2 = -2}$ , so ${(q)^{-2} = q^{-2}}$ In the denominator, we can use the distributive property of exponents. ${q^{-5}a^{2} = q^{-5}a^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(q)^{-2}}}{{q^{-5}a^{2}}} = \dfrac{{q^{-2}}}{{q^{-5}a^{2}}}$ Break up the equation by variable and simplify. $\dfrac{{q^{-2}}}{{q^{-5}a^{2}}} = \dfrac{{q^{-2}}}{{q^{-5}}} \cdot \dfrac{{1}}{{a^{2}}} = q^{{-2} - {(-5)}} \cdot a^{- {2}} = q^{3}a^{-2}$.